Bounds on the Threshold Gap in Secret Sharing and its Applications

@article{Cascudo2013BoundsOT,
  title={Bounds on the Threshold Gap in Secret Sharing and its Applications},
  author={Ignacio Cascudo and Ronald Cramer and Chaoping Xing},
  journal={IEEE Transactions on Information Theory},
  year={2013},
  volume={59},
  pages={5600-5612}
}
We consider the class of secret sharing schemes where there is no a priori bound on the number of players n but where each of the n share-spaces has fixed cardinality q. We show two fundamental lower bounds on the threshold gap of such schemes. The threshold gap g is defined as r-t, where r is minimal and t is maximal such that the following holds: for a secret with arbitrary a priori distribution, each r-subset of players can reconstruct this secret from their joint shares without error ( r… CONTINUE READING

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